Acosta "must step down," she said in a tweet late Monday night.
"As US Attorney, he engaged in an unconscionable agreement with Jeffrey Epstein kept secret from courageous, young victims preventing them from seeking justice," she wrote, adding that Trump was aware of the deal when he appointed Acosta to his Cabinet.
White House senior adviser Kellyanne Conway told reporters on Tuesday that Acosta was "doing a great job."
She downplayed attention on his role in the case, saying the focus should be on Epstein. Asked if the president had confidence in Acosta, Conway pointed to the strength of the US economy.
Representatives for Acosta did not immediately respond to a request for comment.
On Monday, US prosecutors in New York accused Epstein, 66, of sex trafficking in an indictment that detailed how he lured dozens of girls, some as young as 14, to his luxury homes and coerced them into performing sex acts. Epstein has pleaded not guilty.
The prosecutors said they were not bound by the 2008 Florida deal struck by Acosta, then the US Attorney for the Southern District of Florida, that allowed Epstein to plea to a lesser offense. Epstein served 13 months in jail with leave during the day and registered as a sex offender.
Epstein's case drew renewed attention earlier this year after a Miami Herald report highlighted the plea deal and victims' ongoing struggle for justice. In February, a federal judge in Florida ruled that the agreement between Acosta and Epstein violated the victims' rights.
The White House at the time said it was looking into the matter.Acosta's role in the Florida deal for Epstein was raised at his confirmation hearing in the Republican-led Senate. He has served as Labor secretary since April 2017.